Normal-Distortion-Mode Approach to Liquid Crystal Elastic Energy

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Abstract

It is shown that Frank’s ‘‘saddle’’ distortion contribution to the nematic liquid-crystal distortional elastic energy is required, in addition to the splay, twist, and bend energies retained in more recent treatments. ‘‘Normal distortion modes’’ for these four distortions are described. Measurement methods and their interpretations are discussed for the corresponding four elastic constants k11 (splay), k22 (twist), k33 (bend), and k44 (saddle). Previously reported values for k11 and k22 are actually for k11+k44 and k22+k44 respectively. The Nehring-Saupe molecular approach yields k44=(1/2(k11+k22).